Checking for closed mesh
I created a facsimile of your scene to illustrate how this can be done. Here is what I start with.

Next, I create some non-manifold geometry so that I can later illustrate how to expose it. In Edit Mode, I select the edges highlighted below, and peform an Edge Split.

Next, while still in Edit Mode, I go to the Select menu, and Choose Select All by Trait &gt; Non Manifold. This will select all geometry that is not closed.

Very handy. Here is the result.